Properties

Label 1386.2.r.c.1277.3
Level $1386$
Weight $2$
Character 1386.1277
Analytic conductor $11.067$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1277.3
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1386.1277
Dual form 1386.2.r.c.89.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.741181 + 1.28376i) q^{5} +(-1.48356 - 2.19067i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.741181 + 1.28376i) q^{5} +(-1.48356 - 2.19067i) q^{7} -1.00000i q^{8} +(1.28376 + 0.741181i) q^{10} +(0.866025 + 0.500000i) q^{11} +2.44949i q^{13} +(-2.38014 - 1.15539i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.182163 + 0.315515i) q^{17} +(7.06350 - 4.07812i) q^{19} +1.48236 q^{20} +1.00000 q^{22} +(5.18034 - 2.99087i) q^{23} +(1.40130 - 2.42713i) q^{25} +(1.22474 + 2.12132i) q^{26} +(-2.63896 + 0.189469i) q^{28} +0.332449i q^{29} +(0.752011 + 0.434174i) q^{31} +(-0.866025 - 0.500000i) q^{32} +0.364326i q^{34} +(1.71271 - 3.52823i) q^{35} +(-4.64394 - 8.04354i) q^{37} +(4.07812 - 7.06350i) q^{38} +(1.28376 - 0.741181i) q^{40} +9.38891 q^{41} -2.94406 q^{43} +(0.866025 - 0.500000i) q^{44} +(2.99087 - 5.18034i) q^{46} +(-0.637756 - 1.10463i) q^{47} +(-2.59808 + 6.50000i) q^{49} -2.80260i q^{50} +(2.12132 + 1.22474i) q^{52} +(4.65722 + 2.68885i) q^{53} +1.48236i q^{55} +(-2.19067 + 1.48356i) q^{56} +(0.166225 + 0.287909i) q^{58} +(4.43916 - 7.68885i) q^{59} +(-7.28945 + 4.20857i) q^{61} +0.868348 q^{62} -1.00000 q^{64} +(-3.14456 + 1.81552i) q^{65} +(-5.08044 + 8.79958i) q^{67} +(0.182163 + 0.315515i) q^{68} +(-0.280861 - 3.91189i) q^{70} -2.07911i q^{71} +(-7.86798 - 4.54258i) q^{73} +(-8.04354 - 4.64394i) q^{74} -8.15623i q^{76} +(-0.189469 - 2.63896i) q^{77} +(3.00913 + 5.21197i) q^{79} +(0.741181 - 1.28376i) q^{80} +(8.13103 - 4.69445i) q^{82} +15.5699 q^{83} -0.540062 q^{85} +(-2.54963 + 1.47203i) q^{86} +(0.500000 - 0.866025i) q^{88} +(0.459822 + 0.796435i) q^{89} +(5.36603 - 3.63397i) q^{91} -5.98174i q^{92} +(-1.10463 - 0.637756i) q^{94} +(10.4707 + 6.04524i) q^{95} +1.79920i q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + 8q^{5} + O(q^{10}) \) \( 8q + 4q^{4} + 8q^{5} - 4q^{16} - 4q^{17} + 24q^{19} + 16q^{20} + 8q^{22} + 24q^{23} - 4q^{25} + 12q^{31} + 16q^{35} + 12q^{37} - 8q^{38} + 16q^{41} - 32q^{43} + 8q^{46} + 48q^{53} - 4q^{58} + 16q^{59} + 24q^{62} - 8q^{64} - 12q^{65} - 24q^{67} + 4q^{68} - 20q^{70} - 24q^{73} - 12q^{74} + 40q^{79} + 8q^{80} + 12q^{82} + 72q^{83} - 32q^{85} - 24q^{86} + 4q^{88} - 16q^{89} + 36q^{91} + 24q^{95} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
</
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.741181 + 1.28376i 0.331466 + 0.574116i 0.982800 0.184675i \(-0.0591234\pi\)
−0.651333 + 0.758792i \(0.725790\pi\)
\(6\) 0 0
\(7\) −1.48356 2.19067i −0.560734 0.827996i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.28376 + 0.741181i 0.405962 + 0.234382i
\(11\) 0.866025 + 0.500000i 0.261116 + 0.150756i
\(12\) 0 0
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) −2.38014 1.15539i −0.636119 0.308792i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.182163 + 0.315515i −0.0441810 + 0.0765237i −0.887270 0.461250i \(-0.847401\pi\)
0.843089 + 0.537774i \(0.180734\pi\)
\(18\) 0 0
\(19\) 7.06350 4.07812i 1.62048 0.935584i 0.633687 0.773589i \(-0.281541\pi\)
0.986792 0.161995i \(-0.0517928\pi\)
\(20\) 1.48236 0.331466
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 5.18034 2.99087i 1.08018 0.623639i 0.149232 0.988802i \(-0.452320\pi\)
0.930944 + 0.365163i \(0.118987\pi\)
\(24\) 0 0
\(25\) 1.40130 2.42713i 0.280260 0.485425i
\(26\) 1.22474 + 2.12132i 0.240192 + 0.416025i
\(27\) 0 0
\(28\) −2.63896 + 0.189469i −0.498716 + 0.0358062i
\(29\) 0.332449i 0.0617343i 0.999523 + 0.0308671i \(0.00982687\pi\)
−0.999523 + 0.0308671i \(0.990173\pi\)
\(30\) 0 0
\(31\) 0.752011 + 0.434174i 0.135065 + 0.0779799i 0.566010 0.824398i \(-0.308486\pi\)
−0.430945 + 0.902378i \(0.641820\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 0.364326i 0.0624813i
\(35\) 1.71271 3.52823i 0.289501 0.596379i
\(36\) 0 0
\(37\) −4.64394 8.04354i −0.763459 1.32235i −0.941057 0.338247i \(-0.890166\pi\)
0.177598 0.984103i \(-0.443167\pi\)
\(38\) 4.07812 7.06350i 0.661558 1.14585i
\(39\) 0 0
\(40\) 1.28376 0.741181i 0.202981 0.117191i
\(41\) 9.38891 1.46630 0.733150 0.680067i \(-0.238049\pi\)
0.733150 + 0.680067i \(0.238049\pi\)
\(42\) 0 0
\(43\) −2.94406 −0.448965 −0.224482 0.974478i \(-0.572069\pi\)
−0.224482 + 0.974478i \(0.572069\pi\)
\(44\) 0.866025 0.500000i 0.130558 0.0753778i
\(45\) 0 0
\(46\) 2.99087 5.18034i 0.440980 0.763799i
\(47\) −0.637756 1.10463i −0.0930263 0.161126i 0.815757 0.578395i \(-0.196321\pi\)
−0.908783 + 0.417269i \(0.862987\pi\)
\(48\) 0 0
\(49\) −2.59808 + 6.50000i −0.371154 + 0.928571i
\(50\) 2.80260i 0.396348i
\(51\) 0 0
\(52\) 2.12132 + 1.22474i 0.294174 + 0.169842i
\(53\) 4.65722 + 2.68885i 0.639718 + 0.369341i 0.784506 0.620121i \(-0.212917\pi\)
−0.144788 + 0.989463i \(0.546250\pi\)
\(54\) 0 0
\(55\) 1.48236i 0.199882i
\(56\) −2.19067 + 1.48356i −0.292741 + 0.198250i
\(57\) 0 0
\(58\) 0.166225 + 0.287909i 0.0218264 + 0.0378044i
\(59\) 4.43916 7.68885i 0.577929 1.00100i −0.417788 0.908545i \(-0.637194\pi\)
0.995717 0.0924578i \(-0.0294723\pi\)
\(60\) 0 0
\(61\) −7.28945 + 4.20857i −0.933319 + 0.538852i −0.887860 0.460114i \(-0.847808\pi\)
−0.0454590 + 0.998966i \(0.514475\pi\)
\(62\) 0.868348 0.110280
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −3.14456 + 1.81552i −0.390035 + 0.225187i
\(66\) 0 0
\(67\) −5.08044 + 8.79958i −0.620674 + 1.07504i 0.368686 + 0.929554i \(0.379808\pi\)
−0.989360 + 0.145485i \(0.953526\pi\)
\(68\) 0.182163 + 0.315515i 0.0220905 + 0.0382618i
\(69\) 0 0
\(70\) −0.280861 3.91189i −0.0335693 0.467560i
\(71\) 2.07911i 0.246745i −0.992360 0.123373i \(-0.960629\pi\)
0.992360 0.123373i \(-0.0393710\pi\)
\(72\) 0 0
\(73\) −7.86798 4.54258i −0.920878 0.531669i −0.0369628 0.999317i \(-0.511768\pi\)
−0.883915 + 0.467648i \(0.845102\pi\)
\(74\) −8.04354 4.64394i −0.935043 0.539847i
\(75\) 0 0
\(76\) 8.15623i 0.935584i
\(77\) −0.189469 2.63896i −0.0215920 0.300737i
\(78\) 0 0
\(79\) 3.00913 + 5.21197i 0.338554 + 0.586392i 0.984161 0.177278i \(-0.0567290\pi\)
−0.645607 + 0.763670i \(0.723396\pi\)
\(80\) 0.741181 1.28376i 0.0828665 0.143529i
\(81\) 0 0
\(82\) 8.13103 4.69445i 0.897922 0.518416i
\(83\) 15.5699 1.70902 0.854511 0.519433i \(-0.173857\pi\)
0.854511 + 0.519433i \(0.173857\pi\)
\(84\) 0 0
\(85\) −0.540062 −0.0585780
\(86\) −2.54963 + 1.47203i −0.274934 + 0.158733i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 0.459822 + 0.796435i 0.0487410 + 0.0844219i 0.889367 0.457195i \(-0.151146\pi\)
−0.840626 + 0.541617i \(0.817812\pi\)
\(90\) 0 0
\(91\) 5.36603 3.63397i 0.562512 0.380944i
\(92\) 5.98174i 0.623639i
\(93\) 0 0
\(94\) −1.10463 0.637756i −0.113934 0.0657796i
\(95\) 10.4707 + 6.04524i 1.07427 + 0.620229i
\(96\) 0 0
\(97\) 1.79920i 0.182681i 0.995820 + 0.0913407i \(0.0291152\pi\)
−0.995820 + 0.0913407i \(0.970885\pi\)
\(98\) 1.00000 + 6.92820i 0.101015 + 0.699854i
\(99\) 0 0
\(100\) −1.40130 2.42713i −0.140130 0.242713i
\(101\) −5.31079 + 9.19856i −0.528443 + 0.915291i 0.471007 + 0.882130i \(0.343891\pi\)
−0.999450 + 0.0331610i \(0.989443\pi\)
\(102\) 0 0
\(103\) 2.50133 1.44414i 0.246463 0.142295i −0.371681 0.928361i \(-0.621218\pi\)
0.618144 + 0.786065i \(0.287885\pi\)
\(104\) 2.44949 0.240192
\(105\) 0 0
\(106\) 5.37769 0.522328
\(107\) −4.29850 + 2.48174i −0.415552 + 0.239919i −0.693172 0.720772i \(-0.743787\pi\)
0.277621 + 0.960691i \(0.410454\pi\)
\(108\) 0 0
\(109\) 2.23351 3.86855i 0.213932 0.370540i −0.739010 0.673694i \(-0.764706\pi\)
0.952942 + 0.303154i \(0.0980397\pi\)
\(110\) 0.741181 + 1.28376i 0.0706688 + 0.122402i
\(111\) 0 0
\(112\) −1.15539 + 2.38014i −0.109175 + 0.224902i
\(113\) 8.35827i 0.786280i −0.919479 0.393140i \(-0.871389\pi\)
0.919479 0.393140i \(-0.128611\pi\)
\(114\) 0 0
\(115\) 7.67914 + 4.43355i 0.716083 + 0.413431i
\(116\) 0.287909 + 0.166225i 0.0267317 + 0.0154336i
\(117\) 0 0
\(118\) 8.87832i 0.817315i
\(119\) 0.961440 0.0690283i 0.0881350 0.00632781i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) −4.20857 + 7.28945i −0.381026 + 0.659956i
\(123\) 0 0
\(124\) 0.752011 0.434174i 0.0675326 0.0389900i
\(125\) 11.5663 1.03452
\(126\) 0 0
\(127\) −18.1879 −1.61391 −0.806956 0.590612i \(-0.798886\pi\)
−0.806956 + 0.590612i \(0.798886\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −1.81552 + 3.14456i −0.159231 + 0.275797i
\(131\) 9.24264 + 16.0087i 0.807533 + 1.39869i 0.914567 + 0.404433i \(0.132531\pi\)
−0.107034 + 0.994255i \(0.534135\pi\)
\(132\) 0 0
\(133\) −19.4130 9.42367i −1.68332 0.817135i
\(134\) 10.1609i 0.877766i
\(135\) 0 0
\(136\) 0.315515 + 0.182163i 0.0270552 + 0.0156203i
\(137\) −13.8248 7.98174i −1.18113 0.681926i −0.224855 0.974392i \(-0.572191\pi\)
−0.956276 + 0.292466i \(0.905524\pi\)
\(138\) 0 0
\(139\) 9.59111i 0.813507i 0.913538 + 0.406754i \(0.133339\pi\)
−0.913538 + 0.406754i \(0.866661\pi\)
\(140\) −2.19918 3.24737i −0.185865 0.274453i
\(141\) 0 0
\(142\) −1.03956 1.80056i −0.0872376 0.151100i
\(143\) −1.22474 + 2.12132i −0.102418 + 0.177394i
\(144\) 0 0
\(145\) −0.426786 + 0.246405i −0.0354426 + 0.0204628i
\(146\) −9.08516 −0.751894
\(147\) 0 0
\(148\) −9.28788 −0.763459
\(149\) −17.4212 + 10.0582i −1.42720 + 0.823996i −0.996899 0.0786878i \(-0.974927\pi\)
−0.430304 + 0.902684i \(0.641594\pi\)
\(150\) 0 0
\(151\) 2.54466 4.40749i 0.207082 0.358676i −0.743712 0.668500i \(-0.766937\pi\)
0.950794 + 0.309824i \(0.100270\pi\)
\(152\) −4.07812 7.06350i −0.330779 0.572926i
\(153\) 0 0
\(154\) −1.48356 2.19067i −0.119549 0.176529i
\(155\) 1.28721i 0.103391i
\(156\) 0 0
\(157\) −13.7026 7.91119i −1.09358 0.631381i −0.159056 0.987270i \(-0.550845\pi\)
−0.934529 + 0.355888i \(0.884178\pi\)
\(158\) 5.21197 + 3.00913i 0.414642 + 0.239394i
\(159\) 0 0
\(160\) 1.48236i 0.117191i
\(161\) −14.2374 6.91127i −1.12206 0.544684i
\(162\) 0 0
\(163\) 8.89595 + 15.4082i 0.696785 + 1.20687i 0.969575 + 0.244793i \(0.0787201\pi\)
−0.272790 + 0.962073i \(0.587947\pi\)
\(164\) 4.69445 8.13103i 0.366575 0.634927i
\(165\) 0 0
\(166\) 13.4840 7.78497i 1.04656 0.604230i
\(167\) 12.7627 0.987606 0.493803 0.869574i \(-0.335606\pi\)
0.493803 + 0.869574i \(0.335606\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) −0.467708 + 0.270031i −0.0358715 + 0.0207104i
\(171\) 0 0
\(172\) −1.47203 + 2.54963i −0.112241 + 0.194407i
\(173\) 0.636379 + 1.10224i 0.0483830 + 0.0838018i 0.889203 0.457514i \(-0.151260\pi\)
−0.840820 + 0.541315i \(0.817927\pi\)
\(174\) 0 0
\(175\) −7.39595 + 0.531006i −0.559082 + 0.0401402i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) 0.796435 + 0.459822i 0.0596953 + 0.0344651i
\(179\) −7.10671 4.10306i −0.531180 0.306677i 0.210317 0.977633i \(-0.432551\pi\)
−0.741497 + 0.670956i \(0.765884\pi\)
\(180\) 0 0
\(181\) 3.53125i 0.262476i 0.991351 + 0.131238i \(0.0418952\pi\)
−0.991351 + 0.131238i \(0.958105\pi\)
\(182\) 2.83013 5.83013i 0.209783 0.432158i
\(183\) 0 0
\(184\) −2.99087 5.18034i −0.220490 0.381900i
\(185\) 6.88400 11.9234i 0.506122 0.876629i
\(186\) 0 0
\(187\) −0.315515 + 0.182163i −0.0230728 + 0.0133211i
\(188\) −1.27551 −0.0930263
\(189\) 0 0
\(190\) 12.0905 0.877136
\(191\) −3.03516 + 1.75235i −0.219616 + 0.126796i −0.605773 0.795638i \(-0.707136\pi\)
0.386156 + 0.922433i \(0.373803\pi\)
\(192\) 0 0
\(193\) 10.2639 17.7777i 0.738814 1.27966i −0.214215 0.976786i \(-0.568719\pi\)
0.953030 0.302877i \(-0.0979473\pi\)
\(194\) 0.899602 + 1.55816i 0.0645876 + 0.111869i
\(195\) 0 0
\(196\) 4.33013 + 5.50000i 0.309295 + 0.392857i
\(197\) 25.2772i 1.80093i 0.434934 + 0.900463i \(0.356772\pi\)
−0.434934 + 0.900463i \(0.643228\pi\)
\(198\) 0 0
\(199\) −18.4746 10.6663i −1.30963 0.756114i −0.327595 0.944818i \(-0.606238\pi\)
−0.982034 + 0.188704i \(0.939571\pi\)
\(200\) −2.42713 1.40130i −0.171624 0.0990870i
\(201\) 0 0
\(202\) 10.6216i 0.747332i
\(203\) 0.728287 0.493210i 0.0511157 0.0346165i
\(204\) 0 0
\(205\) 6.95888 + 12.0531i 0.486029 + 0.841827i
\(206\) 1.44414 2.50133i 0.100618 0.174276i
\(207\) 0 0
\(208\) 2.12132 1.22474i 0.147087 0.0849208i
\(209\) 8.15623 0.564178
\(210\) 0 0
\(211\) −27.8630 −1.91817 −0.959083 0.283125i \(-0.908629\pi\)
−0.959083 + 0.283125i \(0.908629\pi\)
\(212\) 4.65722 2.68885i 0.319859 0.184671i
\(213\) 0 0
\(214\) −2.48174 + 4.29850i −0.169648 + 0.293839i
\(215\) −2.18208 3.77947i −0.148817 0.257758i
\(216\) 0 0
\(217\) −0.164525 2.29153i −0.0111687 0.155559i
\(218\) 4.46702i 0.302545i
\(219\) 0 0
\(220\) 1.28376 + 0.741181i 0.0865513 + 0.0499704i
\(221\) −0.772851 0.446206i −0.0519876 0.0300151i
\(222\) 0 0
\(223\) 5.97418i 0.400060i 0.979790 + 0.200030i \(0.0641040\pi\)
−0.979790 + 0.200030i \(0.935896\pi\)
\(224\) 0.189469 + 2.63896i 0.0126594 + 0.176323i
\(225\) 0 0
\(226\) −4.17914 7.23848i −0.277992 0.481496i
\(227\) −1.77721 + 3.07822i −0.117958 + 0.204309i −0.918958 0.394355i \(-0.870968\pi\)
0.801000 + 0.598664i \(0.204301\pi\)
\(228\) 0 0
\(229\) 8.68046 5.01167i 0.573621 0.331180i −0.184973 0.982744i \(-0.559220\pi\)
0.758594 + 0.651563i \(0.225886\pi\)
\(230\) 8.86710 0.584679
\(231\) 0 0
\(232\) 0.332449 0.0218264
\(233\) −15.1427 + 8.74264i −0.992031 + 0.572749i −0.905881 0.423533i \(-0.860790\pi\)
−0.0861503 + 0.996282i \(0.527457\pi\)
\(234\) 0 0
\(235\) 0.945386 1.63746i 0.0616702 0.106816i
\(236\) −4.43916 7.68885i −0.288965 0.500501i
\(237\) 0 0
\(238\) 0.798117 0.540500i 0.0517343 0.0350354i
\(239\) 13.9742i 0.903914i 0.892040 + 0.451957i \(0.149274\pi\)
−0.892040 + 0.451957i \(0.850726\pi\)
\(240\) 0 0
\(241\) −0.247649 0.142980i −0.0159525 0.00921018i 0.492003 0.870594i \(-0.336265\pi\)
−0.507955 + 0.861384i \(0.669598\pi\)
\(242\) 0.866025 + 0.500000i 0.0556702 + 0.0321412i
\(243\) 0 0
\(244\) 8.41713i 0.538852i
\(245\) −10.2701 + 1.48236i −0.656133 + 0.0947046i
\(246\) 0 0
\(247\) 9.98930 + 17.3020i 0.635604 + 1.10090i
\(248\) 0.434174 0.752011i 0.0275701 0.0477527i
\(249\) 0 0
\(250\) 10.0167 5.78314i 0.633511 0.365758i
\(251\) −4.29150 −0.270877 −0.135438 0.990786i \(-0.543244\pi\)
−0.135438 + 0.990786i \(0.543244\pi\)
\(252\) 0 0
\(253\) 5.98174 0.376069
\(254\) −15.7511 + 9.09393i −0.988315 + 0.570604i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.88865 + 11.9315i 0.429702 + 0.744266i 0.996847 0.0793525i \(-0.0252853\pi\)
−0.567145 + 0.823618i \(0.691952\pi\)
\(258\) 0 0
\(259\) −10.7312 + 22.1065i −0.666803 + 1.37363i
\(260\) 3.63103i 0.225187i
\(261\) 0 0
\(262\) 16.0087 + 9.24264i 0.989022 + 0.571012i
\(263\) 4.92134 + 2.84134i 0.303463 + 0.175204i 0.643998 0.765028i \(-0.277275\pi\)
−0.340535 + 0.940232i \(0.610608\pi\)
\(264\) 0 0
\(265\) 7.97169i 0.489697i
\(266\) −21.5240 + 1.54535i −1.31972 + 0.0947515i
\(267\) 0 0
\(268\) 5.08044 + 8.79958i 0.310337 + 0.537520i
\(269\) 6.83328 11.8356i 0.416632 0.721628i −0.578966 0.815352i \(-0.696544\pi\)
0.995598 + 0.0937234i \(0.0298769\pi\)
\(270\) 0 0
\(271\) 15.5431 8.97381i 0.944176 0.545120i 0.0529090 0.998599i \(-0.483151\pi\)
0.891267 + 0.453479i \(0.149817\pi\)
\(272\) 0.364326 0.0220905
\(273\) 0 0
\(274\) −15.9635 −0.964389
\(275\) 2.42713 1.40130i 0.146361 0.0845017i
\(276\) 0 0
\(277\) −8.33814 + 14.4421i −0.500990 + 0.867740i 0.499009 + 0.866597i \(0.333697\pi\)
−0.999999 + 0.00114365i \(0.999636\pi\)
\(278\) 4.79555 + 8.30614i 0.287618 + 0.498169i
\(279\) 0 0
\(280\) −3.52823 1.71271i −0.210852 0.102354i
\(281\) 13.1377i 0.783730i 0.920023 + 0.391865i \(0.128170\pi\)
−0.920023 + 0.391865i \(0.871830\pi\)
\(282\) 0 0
\(283\) 25.2985 + 14.6061i 1.50384 + 0.868242i 0.999990 + 0.00444975i \(0.00141641\pi\)
0.503849 + 0.863792i \(0.331917\pi\)
\(284\) −1.80056 1.03956i −0.106844 0.0616863i
\(285\) 0 0
\(286\) 2.44949i 0.144841i
\(287\) −13.9290 20.5680i −0.822205 1.21409i
\(288\) 0 0
\(289\) 8.43363 + 14.6075i 0.496096 + 0.859264i
\(290\) −0.246405 + 0.426786i −0.0144694 + 0.0250617i
\(291\) 0 0
\(292\) −7.86798 + 4.54258i −0.460439 + 0.265835i
\(293\) −25.6875 −1.50068 −0.750339 0.661053i \(-0.770110\pi\)
−0.750339 + 0.661053i \(0.770110\pi\)
\(294\) 0 0
\(295\) 13.1609 0.766256
\(296\) −8.04354 + 4.64394i −0.467521 + 0.269924i
\(297\) 0 0
\(298\) −10.0582 + 17.4212i −0.582653 + 1.00919i
\(299\) 7.32611 + 12.6892i 0.423680 + 0.733835i
\(300\) 0 0
\(301\) 4.36770 + 6.44946i 0.251750 + 0.371741i
\(302\) 5.08933i 0.292858i
\(303\) 0 0
\(304\) −7.06350 4.07812i −0.405120 0.233896i
\(305\) −10.8056 6.23862i −0.618727 0.357222i
\(306\) 0 0
\(307\) 0.928932i 0.0530170i −0.999649 0.0265085i \(-0.991561\pi\)
0.999649 0.0265085i \(-0.00843890\pi\)
\(308\) −2.38014 1.15539i −0.135621 0.0658347i
\(309\) 0 0
\(310\) 0.643603 + 1.11475i 0.0365542 + 0.0633137i
\(311\) 4.63676 8.03111i 0.262927 0.455402i −0.704092 0.710109i \(-0.748646\pi\)
0.967018 + 0.254707i \(0.0819790\pi\)
\(312\) 0 0
\(313\) −0.884368 + 0.510590i −0.0499874 + 0.0288602i −0.524785 0.851235i \(-0.675854\pi\)
0.474798 + 0.880095i \(0.342521\pi\)
\(314\) −15.8224 −0.892908
\(315\) 0 0
\(316\) 6.01826 0.338554
\(317\) 9.92460 5.72997i 0.557421 0.321827i −0.194689 0.980865i \(-0.562370\pi\)
0.752110 + 0.659038i \(0.229036\pi\)
\(318\) 0 0
\(319\) −0.166225 + 0.287909i −0.00930679 + 0.0161198i
\(320\) −0.741181 1.28376i −0.0414333 0.0717645i
\(321\) 0 0
\(322\) −15.7856 + 1.13335i −0.879695 + 0.0631593i
\(323\) 2.97152i 0.165340i
\(324\) 0 0
\(325\) 5.94522 + 3.43247i 0.329781 + 0.190399i
\(326\) 15.4082 + 8.89595i 0.853384 + 0.492701i
\(327\) 0 0
\(328\) 9.38891i 0.518416i
\(329\) −1.47372 + 3.03590i −0.0812488 + 0.167374i
\(330\) 0 0
\(331\) 10.9670 + 18.9954i 0.602802 + 1.04408i 0.992395 + 0.123096i \(0.0392824\pi\)
−0.389593 + 0.920987i \(0.627384\pi\)
\(332\) 7.78497 13.4840i 0.427255 0.740028i
\(333\) 0 0
\(334\) 11.0528 6.38134i 0.604783 0.349171i
\(335\) −15.0621 −0.822930
\(336\) 0 0
\(337\) −10.7768 −0.587049 −0.293524 0.955952i \(-0.594828\pi\)
−0.293524 + 0.955952i \(0.594828\pi\)
\(338\) 6.06218 3.50000i 0.329739 0.190375i
\(339\) 0 0
\(340\) −0.270031 + 0.467708i −0.0146445 + 0.0253650i
\(341\) 0.434174 + 0.752011i 0.0235118 + 0.0407237i
\(342\) 0 0
\(343\) 18.0938 3.95164i 0.976972 0.213368i
\(344\) 2.94406i 0.158733i
\(345\) 0 0
\(346\) 1.10224 + 0.636379i 0.0592568 + 0.0342119i
\(347\) −27.5550 15.9089i −1.47923 0.854033i −0.479504 0.877540i \(-0.659183\pi\)
−0.999724 + 0.0235069i \(0.992517\pi\)
\(348\) 0 0
\(349\) 20.3088i 1.08711i 0.839375 + 0.543553i \(0.182921\pi\)
−0.839375 + 0.543553i \(0.817079\pi\)
\(350\) −6.13958 + 4.15784i −0.328174 + 0.222246i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −6.06314 + 10.5017i −0.322708 + 0.558947i −0.981046 0.193776i \(-0.937927\pi\)
0.658338 + 0.752723i \(0.271260\pi\)
\(354\) 0 0
\(355\) 2.66909 1.54100i 0.141660 0.0817877i
\(356\) 0.919644 0.0487410
\(357\) 0 0
\(358\) −8.20612 −0.433707
\(359\) −11.6763 + 6.74131i −0.616251 + 0.355793i −0.775408 0.631460i \(-0.782456\pi\)
0.159157 + 0.987253i \(0.449123\pi\)
\(360\) 0 0
\(361\) 23.7621 41.1571i 1.25063 2.16616i
\(362\) 1.76563 + 3.05816i 0.0927993 + 0.160733i
\(363\) 0 0
\(364\) −0.464102 6.46410i −0.0243255 0.338811i
\(365\) 13.4675i 0.704921i
\(366\) 0 0
\(367\) −27.0615 15.6240i −1.41260 0.815565i −0.416968 0.908921i \(-0.636907\pi\)
−0.995633 + 0.0933561i \(0.970240\pi\)
\(368\) −5.18034 2.99087i −0.270044 0.155910i
\(369\) 0 0
\(370\) 13.7680i 0.715765i
\(371\) −1.01890 14.1915i −0.0528989 0.736786i
\(372\) 0 0
\(373\) −0.444639 0.770138i −0.0230226 0.0398762i 0.854285 0.519806i \(-0.173996\pi\)
−0.877307 + 0.479929i \(0.840662\pi\)
\(374\) −0.182163 + 0.315515i −0.00941941 + 0.0163149i
\(375\) 0 0
\(376\) −1.10463 + 0.637756i −0.0569668 + 0.0328898i
\(377\) −0.814331 −0.0419402
\(378\) 0 0
\(379\) 20.9635 1.07682 0.538411 0.842683i \(-0.319025\pi\)
0.538411 + 0.842683i \(0.319025\pi\)
\(380\) 10.4707 6.04524i 0.537134 0.310114i
\(381\) 0 0
\(382\) −1.75235 + 3.03516i −0.0896581 + 0.155292i
\(383\) −0.824147 1.42747i −0.0421120 0.0729401i 0.844201 0.536026i \(-0.180075\pi\)
−0.886313 + 0.463086i \(0.846742\pi\)
\(384\) 0 0
\(385\) 3.24737 2.19918i 0.165501 0.112081i
\(386\) 20.5279i 1.04484i
\(387\) 0 0
\(388\) 1.55816 + 0.899602i 0.0791034 + 0.0456704i
\(389\) 7.89537 + 4.55840i 0.400311 + 0.231120i 0.686618 0.727018i \(-0.259094\pi\)
−0.286307 + 0.958138i \(0.592428\pi\)
\(390\) 0 0
\(391\) 2.17930i 0.110212i
\(392\) 6.50000 + 2.59808i 0.328300 + 0.131223i
\(393\) 0 0
\(394\) 12.6386 + 21.8907i 0.636723 + 1.10284i
\(395\) −4.46062 + 7.72602i −0.224438 + 0.388738i
\(396\) 0 0
\(397\) 6.49063 3.74737i 0.325755 0.188075i −0.328200 0.944608i \(-0.606442\pi\)
0.653955 + 0.756533i \(0.273109\pi\)
\(398\) −21.3326 −1.06931
\(399\) 0 0
\(400\) −2.80260 −0.140130
\(401\) −5.45101 + 3.14714i −0.272211 + 0.157161i −0.629892 0.776683i \(-0.716901\pi\)
0.357681 + 0.933844i \(0.383567\pi\)
\(402\) 0 0
\(403\) −1.06350 + 1.84204i −0.0529769 + 0.0917587i
\(404\) 5.31079 + 9.19856i 0.264222 + 0.457645i
\(405\) 0 0
\(406\) 0.384110 0.791275i 0.0190631 0.0392703i
\(407\) 9.28788i 0.460383i
\(408\) 0 0
\(409\) −11.7467 6.78194i −0.580835 0.335345i 0.180630 0.983551i \(-0.442186\pi\)
−0.761465 + 0.648206i \(0.775520\pi\)
\(410\) 12.0531 + 6.95888i 0.595262 + 0.343674i
\(411\) 0 0
\(412\) 2.88828i 0.142295i
\(413\) −23.4295 + 1.68216i −1.15289 + 0.0827738i
\(414\) 0 0
\(415\) 11.5401 + 19.9881i 0.566483 + 0.981177i
\(416\) 1.22474 2.12132i 0.0600481 0.104006i
\(417\) 0 0
\(418\) 7.06350 4.07812i 0.345487 0.199467i
\(419\) 20.4037 0.996785 0.498393 0.866951i \(-0.333924\pi\)
0.498393 + 0.866951i \(0.333924\pi\)
\(420\) 0 0
\(421\) −19.0673 −0.929284 −0.464642 0.885499i \(-0.653817\pi\)
−0.464642 + 0.885499i \(0.653817\pi\)
\(422\) −24.1300 + 13.9315i −1.17463 + 0.678174i
\(423\) 0 0
\(424\) 2.68885 4.65722i 0.130582 0.226175i
\(425\) 0.510530 + 0.884264i 0.0247643 + 0.0428931i
\(426\) 0 0
\(427\) 20.0339 + 9.72511i 0.969511 + 0.470631i
\(428\) 4.96348i 0.239919i
\(429\) 0 0
\(430\) −3.77947 2.18208i −0.182262 0.105229i
\(431\) 24.1846 + 13.9630i 1.16493 + 0.672574i 0.952481 0.304598i \(-0.0985220\pi\)
0.212451 + 0.977172i \(0.431855\pi\)
\(432\) 0 0
\(433\) 24.8145i 1.19251i −0.802796 0.596254i \(-0.796655\pi\)
0.802796 0.596254i \(-0.203345\pi\)
\(434\) −1.28825 1.90226i −0.0618379 0.0913116i
\(435\) 0 0
\(436\) −2.23351 3.86855i −0.106966 0.185270i
\(437\) 24.3942 42.2520i 1.16693 2.02119i
\(438\) 0 0
\(439\) −12.6859 + 7.32420i −0.605464 + 0.349565i −0.771188 0.636607i \(-0.780337\pi\)
0.165724 + 0.986172i \(0.447004\pi\)
\(440\) 1.48236 0.0706688
\(441\) 0 0
\(442\) −0.892412 −0.0424477
\(443\) −27.7172 + 16.0026i −1.31689 + 0.760304i −0.983226 0.182389i \(-0.941617\pi\)
−0.333659 + 0.942694i \(0.608284\pi\)
\(444\) 0 0
\(445\) −0.681622 + 1.18060i −0.0323120 + 0.0559660i
\(446\) 2.98709 + 5.17379i 0.141443 + 0.244986i
\(447\) 0 0
\(448\) 1.48356 + 2.19067i 0.0700918 + 0.103499i
\(449\) 38.8938i 1.83551i −0.397146 0.917755i \(-0.630000\pi\)
0.397146 0.917755i \(-0.370000\pi\)
\(450\) 0 0
\(451\) 8.13103 + 4.69445i 0.382875 + 0.221053i
\(452\) −7.23848 4.17914i −0.340469 0.196570i
\(453\) 0 0
\(454\) 3.55443i 0.166817i
\(455\) 8.64236 + 4.19527i 0.405160 + 0.196677i
\(456\) 0 0
\(457\) −11.8239 20.4796i −0.553099 0.957995i −0.998049 0.0624396i \(-0.980112\pi\)
0.444950 0.895555i \(-0.353221\pi\)
\(458\) 5.01167 8.68046i 0.234180 0.405611i
\(459\) 0 0
\(460\) 7.67914 4.43355i 0.358042 0.206715i
\(461\) −7.97181 −0.371284 −0.185642 0.982617i \(-0.559436\pi\)
−0.185642 + 0.982617i \(0.559436\pi\)
\(462\) 0 0
\(463\) −33.7108 −1.56667 −0.783337 0.621597i \(-0.786484\pi\)
−0.783337 + 0.621597i \(0.786484\pi\)
\(464\) 0.287909 0.166225i 0.0133659 0.00771678i
\(465\) 0 0
\(466\) −8.74264 + 15.1427i −0.404995 + 0.701472i
\(467\) −9.33814 16.1741i −0.432117 0.748449i 0.564938 0.825133i \(-0.308900\pi\)
−0.997055 + 0.0766840i \(0.975567\pi\)
\(468\) 0 0
\(469\) 26.8141 1.92517i 1.23816 0.0888960i
\(470\) 1.89077i 0.0872148i
\(471\) 0 0
\(472\) −7.68885 4.43916i −0.353908 0.204329i
\(473\) −2.54963 1.47203i −0.117232 0.0676840i
\(474\) 0 0
\(475\) 22.8587i 1.04883i
\(476\) 0.420940 0.867145i 0.0192937 0.0397455i
\(477\) 0 0
\(478\) 6.98709 + 12.1020i 0.319582 + 0.553532i
\(479\) −8.06866 + 13.9753i −0.368667 + 0.638549i −0.989357 0.145506i \(-0.953519\pi\)
0.620691 + 0.784056i \(0.286852\pi\)
\(480\) 0 0
\(481\) 19.7026 11.3753i 0.898360 0.518669i
\(482\) −0.285961 −0.0130252
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −2.30975 + 1.33354i −0.104880 + 0.0605527i
\(486\) 0 0
\(487\) −12.7790 + 22.1339i −0.579072 + 1.00298i 0.416515 + 0.909129i \(0.363251\pi\)
−0.995586 + 0.0938523i \(0.970082\pi\)
\(488\) 4.20857 + 7.28945i 0.190513 + 0.329978i
\(489\) 0 0
\(490\) −8.15299 + 6.41882i −0.368315 + 0.289973i
\(491\) 21.5909i 0.974384i −0.873295 0.487192i \(-0.838021\pi\)
0.873295 0.487192i \(-0.161979\pi\)
\(492\) 0 0
\(493\) −0.104893 0.0605598i −0.00472413 0.00272748i
\(494\) 17.3020 + 9.98930i 0.778453 + 0.449440i
\(495\) 0 0
\(496\) 0.868348i 0.0389900i
\(497\) −4.55465 + 3.08450i −0.204304 + 0.138359i
\(498\) 0 0
\(499\) 0.470154 + 0.814331i 0.0210470 + 0.0364544i 0.876357 0.481662i \(-0.159967\pi\)
−0.855310 + 0.518116i \(0.826633\pi\)
\(500\) 5.78314 10.0167i 0.258630 0.447960i
\(501\) 0 0
\(502\) −3.71655 + 2.14575i −0.165878 + 0.0957695i
\(503\) 37.4660 1.67053 0.835264 0.549849i \(-0.185315\pi\)
0.835264 + 0.549849i \(0.185315\pi\)
\(504\) 0 0
\(505\) −15.7450 −0.700644
\(506\) 5.18034 2.99087i 0.230294 0.132960i
\(507\) 0 0
\(508\) −9.09393 + 15.7511i −0.403478 + 0.698844i
\(509\) 8.52849 + 14.7718i 0.378018 + 0.654747i 0.990774 0.135525i \(-0.0432722\pi\)
−0.612755 + 0.790273i \(0.709939\pi\)
\(510\) 0 0
\(511\) 1.72135 + 23.9754i 0.0761482 + 1.06061i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 11.9315 + 6.88865i 0.526275 + 0.303845i
\(515\) 3.70787 + 2.14074i 0.163388 + 0.0943323i
\(516\) 0 0
\(517\) 1.27551i 0.0560970i
\(518\) 1.75976 + 24.5103i 0.0773196 + 1.07692i
\(519\) 0 0
\(520\) 1.81552 + 3.14456i 0.0796156 + 0.137898i
\(521\) −14.2022 + 24.5989i −0.622210 + 1.07770i 0.366863 + 0.930275i \(0.380432\pi\)
−0.989073 + 0.147424i \(0.952902\pi\)
\(522\) 0 0
\(523\) 13.1571 7.59627i 0.575321 0.332162i −0.183951 0.982935i \(-0.558889\pi\)
0.759272 + 0.650774i \(0.225555\pi\)
\(524\) 18.4853 0.807533
\(525\) 0 0
\(526\) 5.68268 0.247777
\(527\) −0.273977 + 0.158181i −0.0119346 + 0.00689045i
\(528\) 0 0
\(529\) 6.39060 11.0689i 0.277852 0.481254i
\(530\) 3.98584 + 6.90368i 0.173134 + 0.299877i
\(531\) 0 0
\(532\) −17.8676 + 12.1003i −0.774660 + 0.524614i
\(533\) 22.9980i 0.996155i
\(534\) 0 0
\(535\) −6.37193 3.67884i −0.275483 0.159050i
\(536\) 8.79958 + 5.08044i 0.380084 + 0.219442i
\(537\) 0 0
\(538\) 13.6666i 0.589207i
\(539\) −5.50000 + 4.33013i −0.236902 + 0.186512i
\(540\) 0 0
\(541\) −15.8538 27.4597i −0.681610 1.18058i −0.974489 0.224434i \(-0.927947\pi\)
0.292879 0.956149i \(-0.405387\pi\)
\(542\) 8.97381 15.5431i 0.385458 0.667633i
\(543\) 0 0
\(544\) 0.315515 0.182163i 0.0135276 0.00781016i
\(545\) 6.62174 0.283644
\(546\) 0 0
\(547\) −6.10562 −0.261057 −0.130529 0.991445i \(-0.541667\pi\)
−0.130529 + 0.991445i \(0.541667\pi\)
\(548\) −13.8248 + 7.98174i −0.590565 + 0.340963i
\(549\) 0 0
\(550\) 1.40130 2.42713i 0.0597517 0.103493i
\(551\) 1.35577 + 2.34826i 0.0577576 + 0.100039i
\(552\) 0 0
\(553\) 6.95346 14.3243i 0.295691 0.609131i
\(554\) 16.6763i 0.708507i
\(555\) 0 0
\(556\) 8.30614 + 4.79555i 0.352259 + 0.203377i
\(557\) 4.29153 + 2.47772i 0.181838 + 0.104984i 0.588156 0.808748i \(-0.299854\pi\)
−0.406318 + 0.913732i \(0.633187\pi\)
\(558\) 0 0
\(559\) 7.21144i 0.305012i
\(560\) −3.91189 + 0.280861i −0.165308 + 0.0118686i
\(561\) 0 0
\(562\) 6.56885 + 11.3776i 0.277090 + 0.479935i
\(563\) 13.7773 23.8630i 0.580644 1.00570i −0.414759 0.909931i \(-0.636134\pi\)
0.995403 0.0957734i \(-0.0305324\pi\)
\(564\) 0 0
\(565\) 10.7300 6.19499i 0.451416 0.260625i
\(566\) 29.2122 1.22788
\(567\) 0 0
\(568\) −2.07911 −0.0872376
\(569\) −11.0129 + 6.35827i −0.461683 + 0.266553i −0.712752 0.701417i \(-0.752551\pi\)
0.251069 + 0.967969i \(0.419218\pi\)
\(570\) 0 0
\(571\) 20.4985 35.5045i 0.857837 1.48582i −0.0161511 0.999870i \(-0.505141\pi\)
0.873988 0.485948i \(-0.161525\pi\)
\(572\) 1.22474 + 2.12132i 0.0512092 + 0.0886969i
\(573\) 0 0
\(574\) −22.3469 10.8479i −0.932742 0.452782i
\(575\) 16.7644i 0.699126i
\(576\) 0 0
\(577\) −22.1999 12.8171i −0.924193 0.533583i −0.0392228 0.999230i \(-0.512488\pi\)
−0.884970 + 0.465647i \(0.845822\pi\)
\(578\) 14.6075 + 8.43363i 0.607591 + 0.350793i
\(579\) 0 0
\(580\) 0.492810i 0.0204628i
\(581\) −23.0990 34.1086i −0.958307 1.41506i
\(582\) 0 0
\(583\) 2.68885 + 4.65722i 0.111361 + 0.192882i
\(584\) −4.54258 + 7.86798i −0.187973 + 0.325579i
\(585\) 0 0
\(586\) −22.2460 + 12.8437i −0.918974 + 0.530570i
\(587\) 12.7060 0.524433 0.262216 0.965009i \(-0.415547\pi\)
0.262216 + 0.965009i \(0.415547\pi\)
\(588\) 0 0
\(589\) 7.08244 0.291827
\(590\) 11.3977 6.58044i 0.469234 0.270912i
\(591\) 0 0
\(592\) −4.64394 + 8.04354i −0.190865 + 0.330588i
\(593\) 13.4689 + 23.3288i 0.553102 + 0.958000i 0.998049 + 0.0624434i \(0.0198893\pi\)
−0.444947 + 0.895557i \(0.646777\pi\)
\(594\) 0 0
\(595\) 0.801217 + 1.18310i 0.0328467 + 0.0485023i
\(596\) 20.1163i 0.823996i
\(597\) 0 0
\(598\) 12.6892 + 7.32611i 0.518899 + 0.299587i
\(599\) −8.83280 5.09962i −0.360898 0.208365i 0.308576 0.951200i \(-0.400147\pi\)
−0.669475 + 0.742835i \(0.733481\pi\)
\(600\) 0 0
\(601\) 5.89774i 0.240574i −0.992739 0.120287i \(-0.961619\pi\)
0.992739 0.120287i \(-0.0383814\pi\)
\(602\) 7.00727 + 3.40155i 0.285595 + 0.138637i
\(603\) 0 0
\(604\) −2.54466 4.40749i −0.103541 0.179338i
\(605\) −0.741181 + 1.28376i −0.0301333 + 0.0521924i
\(606\) 0 0
\(607\) −23.4361 + 13.5308i −0.951243 + 0.549200i −0.893467 0.449129i \(-0.851734\pi\)
−0.0577759 + 0.998330i \(0.518401\pi\)
\(608\) −8.15623 −0.330779
\(609\) 0 0
\(610\) −12.4772 −0.505189
\(611\) 2.70577 1.56218i 0.109464 0.0631990i
\(612\) 0 0
\(613\) 16.5001 28.5790i 0.666433 1.15430i −0.312462 0.949930i \(-0.601154\pi\)
0.978895 0.204365i \(-0.0655130\pi\)
\(614\) −0.464466 0.804479i −0.0187443 0.0324661i
\(615\) 0 0
\(616\) −2.63896 + 0.189469i −0.106327 + 0.00763391i
\(617\) 26.6032i 1.07101i 0.844533 + 0.535503i \(0.179878\pi\)
−0.844533 + 0.535503i \(0.820122\pi\)
\(618\) 0 0
\(619\) 18.5141 + 10.6891i 0.744143 + 0.429631i 0.823574 0.567209i \(-0.191977\pi\)
−0.0794305 + 0.996840i \(0.525310\pi\)
\(620\) 1.11475 + 0.643603i 0.0447695 + 0.0258477i
\(621\) 0 0
\(622\) 9.27352i 0.371834i
\(623\) 1.06255 2.18888i 0.0425702 0.0876956i
\(624\) 0 0
\(625\) 1.56620 + 2.71274i 0.0626480 + 0.108510i
\(626\) −0.510590 + 0.884368i −0.0204073 + 0.0353464i
\(627\) 0 0
\(628\) −13.7026 + 7.91119i −0.546792 + 0.315691i
\(629\) 3.38381 0.134921
\(630\) 0 0
\(631\) 34.2068 1.36175 0.680876 0.732399i \(-0.261599\pi\)
0.680876 + 0.732399i \(0.261599\pi\)
\(632\) 5.21197 3.00913i 0.207321 0.119697i
\(633\) 0 0
\(634\) 5.72997 9.92460i 0.227566 0.394156i
\(635\) −13.4805 23.3489i −0.534957 0.926573i
\(636\) 0 0
\(637\) −15.9217 6.36396i −0.630840 0.252149i
\(638\) 0.332449i 0.0131618i
\(639\) 0 0
\(640\) −1.28376 0.741181i −0.0507452 0.0292977i
\(641\) −6.68319 3.85854i −0.263970 0.152403i 0.362174 0.932110i \(-0.382035\pi\)
−0.626144 + 0.779707i \(0.715368\pi\)
\(642\) 0 0
\(643\) 31.0411i 1.22414i 0.790803 + 0.612071i \(0.209663\pi\)
−0.790803 + 0.612071i \(0.790337\pi\)
\(644\) −13.1040 + 8.87429i −0.516371 + 0.349696i
\(645\) 0 0
\(646\) 1.48576 + 2.57341i 0.0584565 + 0.101250i
\(647\) 19.7719 34.2460i 0.777315 1.34635i −0.156170 0.987730i \(-0.549915\pi\)
0.933484 0.358618i \(-0.116752\pi\)
\(648\) 0 0
\(649\) 7.68885 4.43916i 0.301814 0.174252i
\(650\) 6.86495 0.269265
\(651\) 0 0
\(652\) 17.7919 0.696785
\(653\) 5.85305 3.37926i 0.229048 0.132241i −0.381085 0.924540i \(-0.624450\pi\)
0.610133 + 0.792299i \(0.291116\pi\)
\(654\) 0 0
\(655\) −13.7009 + 23.7307i −0.535340 + 0.927236i
\(656\) −4.69445 8.13103i −0.183288 0.317463i
\(657\) 0 0
\(658\) 0.241670 + 3.36603i 0.00942127 + 0.131221i
\(659\) 36.2611i 1.41253i 0.707947 + 0.706266i \(0.249622\pi\)
−0.707947 + 0.706266i \(0.750378\pi\)
\(660\) 0 0
\(661\) −26.4271 15.2577i −1.02790 0.593456i −0.111515 0.993763i \(-0.535570\pi\)
−0.916381 + 0.400307i \(0.868904\pi\)
\(662\) 18.9954 + 10.9670i 0.738279 + 0.426245i
\(663\) 0 0
\(664\) 15.5699i 0.604230i
\(665\) −2.29077 31.9063i −0.0888322 1.23727i
\(666\) 0 0
\(667\) 0.994312 + 1.72220i 0.0384999 + 0.0666838i
\(668\) 6.38134 11.0528i 0.246902 0.427646i
\(669\) 0 0
\(670\) −13.0442 + 7.53105i −0.503940 + 0.290950i
\(671\) −8.41713 −0.324940
\(672\) 0 0
\(673\) −18.4702 −0.711972 −0.355986 0.934491i \(-0.615855\pi\)
−0.355986 + 0.934491i \(0.615855\pi\)
\(674\) −9.33296 + 5.38839i −0.359492 + 0.207553i
\(675\) 0 0
\(676\) 3.50000 6.06218i 0.134615 0.233161i
\(677\) 18.9418 + 32.8082i 0.727993 + 1.26092i 0.957730 + 0.287669i \(0.0928801\pi\)
−0.229737 + 0.973253i \(0.573787\pi\)
\(678\) 0 0
\(679\) 3.94146 2.66923i 0.151259 0.102436i
\(680\) 0.540062i 0.0207104i
\(681\) 0 0
\(682\) 0.752011 + 0.434174i 0.0287960 + 0.0166254i
\(683\) 3.63276 + 2.09737i 0.139004 + 0.0802537i 0.567889 0.823105i \(-0.307760\pi\)
−0.428885 + 0.903359i \(0.641094\pi\)
\(684\) 0 0
\(685\) 23.6637i 0.904142i
\(686\) 13.6938 12.4691i 0.522834 0.476073i
\(687\) 0 0
\(688\) 1.47203 + 2.54963i 0.0561206 + 0.0972037i
\(689\) −6.58630 + 11.4078i −0.250918 + 0.434603i
\(690\) 0 0
\(691\) 25.8937 14.9498i 0.985044 0.568716i 0.0812550 0.996693i \(-0.474107\pi\)
0.903789 + 0.427978i \(0.140774\pi\)
\(692\) 1.27276 0.0483830
\(693\) 0 0
\(694\) −31.8177 −1.20778
\(695\) −12.3127 + 7.10875i −0.467048 + 0.269650i
\(696\) 0 0
\(697\) −1.71031 + 2.96234i −0.0647826 + 0.112207i
\(698\) 10.1544 + 17.5879i 0.384350 + 0.665713i
\(699\) 0 0
\(700\) −3.23811 + 6.67059i −0.122389 + 0.252124i
\(701\) 6.63368i 0.250551i −0.992122 0.125275i \(-0.960019\pi\)
0.992122 0.125275i \(-0.0399814\pi\)
\(702\) 0 0
\(703\) −65.6050 37.8771i −2.47434 1.42856i
\(704\) −0.866025 0.500000i −0.0326396 0.0188445i
\(705\) 0 0
\(706\) 12.1263i 0.456379i
\(707\) 28.0299 2.01246i 1.05417 0.0756862i
\(708\) 0 0
\(709\) −9.77143 16.9246i −0.366974 0.635617i 0.622117 0.782924i \(-0.286273\pi\)
−0.989091 + 0.147307i \(0.952939\pi\)
\(710\) 1.54100 2.66909i 0.0578326 0.100169i
\(711\) 0 0
\(712\) 0.796435 0.459822i 0.0298477 0.0172326i
\(713\) 5.19423 0.194525
\(714\) 0 0
\(715\) −3.63103 −0.135793
\(716\) −7.10671 + 4.10306i −0.265590 + 0.153339i
\(717\) 0 0
\(718\) −6.74131 + 11.6763i −0.251584 + 0.435756i
\(719\) 18.5505 + 32.1304i 0.691816 + 1.19826i 0.971242 + 0.238093i \(0.0765223\pi\)
−0.279427 + 0.960167i \(0.590144\pi\)
\(720\) 0 0
\(721\) −6.87452 3.33711i −0.256020 0.124280i
\(722\) 47.5241i 1.76866i
\(723\) 0 0
\(724\) 3.05816 + 1.76563i 0.113655 + 0.0656190i
\(725\) 0.806896 + 0.465861i 0.0299674 + 0.0173017i
\(726\) 0 0
\(727\) 6.35238i 0.235597i 0.993038 + 0.117798i \(0.0375837\pi\)
−0.993038 + 0.117798i \(0.962416\pi\)
\(728\) −3.63397 5.36603i −0.134684 0.198878i
\(729\) 0 0
\(730\) −6.73375 11.6632i −0.249227 0.431674i
\(731\) 0.536298 0.928895i 0.0198357 0.0343564i
\(732\) 0 0
\(733\) −11.6975 + 6.75355i −0.432057 + 0.249448i −0.700223 0.713925i \(-0.746916\pi\)
0.268166 + 0.963373i \(0.413583\pi\)
\(734\) −31.2480 −1.15338
\(735\) 0 0
\(736\) −5.98174 −0.220490
\(737\) −8.79958 + 5.08044i −0.324137 + 0.187140i
\(738\) 0 0
\(739\) 21.1056 36.5560i 0.776383 1.34473i −0.157632 0.987498i \(-0.550386\pi\)
0.934014 0.357236i \(-0.116281\pi\)
\(740\) −6.88400 11.9234i −0.253061 0.438314i
\(741\) 0 0
\(742\) −7.97815 11.7808i −0.292887 0.432485i
\(743\) 44.2670i 1.62400i −0.583657 0.812000i \(-0.698379\pi\)
0.583657 0.812000i \(-0.301621\pi\)
\(744\) 0 0
\(745\) −25.8246 14.9098i −0.946139 0.546254i
\(746\) −0.770138 0.444639i −0.0281968 0.0162794i
\(747\) 0 0
\(748\) 0.364326i 0.0133211i
\(749\) 11.8138 + 5.73478i 0.431666 + 0.209544i
\(750\) 0 0
\(751\) 9.76492 + 16.9133i 0.356327 + 0.617177i 0.987344 0.158592i \(-0.0506955\pi\)
−0.631017 + 0.775769i \(0.717362\pi\)
\(752\) −0.637756 + 1.10463i −0.0232566 + 0.0402816i
\(753\) 0 0
\(754\) −0.705231 + 0.407165i −0.0256830 + 0.0148281i
\(755\) 7.54423 0.274563
\(756\) 0 0
\(757\) 13.7687 0.500433 0.250217 0.968190i \(-0.419498\pi\)
0.250217 + 0.968190i \(0.419498\pi\)
\(758\) 18.1549 10.4817i 0.659416 0.380714i
\(759\) 0 0
\(760\) 6.04524 10.4707i 0.219284 0.379811i
\(761\) −5.03177 8.71528i −0.182402 0.315929i 0.760296 0.649576i \(-0.225054\pi\)
−0.942698 + 0.333648i \(0.891720\pi\)
\(762\) 0 0
\(763\) −11.7883 + 0.846361i −0.426764 + 0.0306403i
\(764\) 3.50470i 0.126796i
\(765\) 0 0
\(766\) −1.42747 0.824147i −0.0515764 0.0297777i
\(767\) 18.8338 + 10.8737i 0.680047 + 0.392626i
\(768\) 0 0
\(769\) 0.355784i 0.0128299i 0.999979 + 0.00641495i \(0.00204196\pi\)
−0.999979 + 0.00641495i \(0.997958\pi\)
\(770\) 1.71271 3.52823i 0.0617219 0.127149i
\(771\) 0 0
\(772\) −10.2639 17.7777i −0.369407 0.639832i
\(773\) 24.7902 42.9379i 0.891642 1.54437i 0.0537365 0.998555i \(-0.482887\pi\)
0.837906 0.545815i \(-0.183780\pi\)
\(774\) 0 0
\(775\) 2.10759 1.21682i 0.0757068 0.0437093i
\(776\) 1.79920 0.0645876
\(777\) 0 0
\(778\) 9.11679 0.326853
\(779\) 66.3186 38.2890i 2.37611 1.37185i
\(780\) 0 0
\(781\) 1.03956 1.80056i 0.0371982 0.0644292i
\(782\) 1.08965 + 1.88733i 0.0389658 + 0.0674908i
\(783\) 0 0
\(784\) 6.92820 1.00000i 0.247436 0.0357143i
\(785\) 23.4545i 0.837126i
\(786\) 0 0
\(787\) −25.9077 14.9578i −0.923511 0.533189i −0.0387576 0.999249i \(-0.512340\pi\)
−0.884754 + 0.466059i \(0.845673\pi\)
\(788\) 21.8907 + 12.6386i 0.779823 + 0.450231i
\(789\) 0 0